Luminal or tubular grafts are placed in native blood vessels and other body lumens to treat various medical conditions, including aneurysms and stenoses. Open surgical procedures can be used to implant such grafts. These procedures, however, can be traumatic for patients and require an extended recovery period. Another approach is to deliver a graft endoluminally through an access or cut down in a vessel remote from the intended graft location. Endoluminal delivery is typically less traumatic for patients than open surgery and requires a shorter recovery period. Endoluminal delivery, however, can be difficult where native vessels provide a tortuous path for delivery. Also, remote vessels typically provide small openings, which may not be large enough to accept an existing graft and delivery system. To overcome the shortcomings of existing grafts and delivery systems, a need exists for a low profile graft configuration for endoluminal delivery.